SSC CGL Tier 2 (19 Feb) Past Year Paper (2018) | SSC CGL (Hindi) Tier - 1 Mock Test Series PDF Download

 Page 1


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 19-2-2018] [Time : 10 AM to 12 PM 
1.  If N = 1+11+111+1111+ .... + 111111111, then 
what is the some of he digit's of N? 
  Option :  
  Ùeefo N = 1+11+111+1111+ .... + 111111111, nes lees 
N kesâ DebkeâeW keâe Ùeesie keäÙee nw? 
 (a) 45 (b) 18  
 (c) 36 (d) 5 
2.  What is he sum of first 40 terms of 
1+3+4+5+7+7+10+9+ .....?  
  1+3+4+5+7+7+10+9+ ..... kesâ ØeLece 40 heoeW keâe Ùeesie 
keäÙee nw?  
 (a) 1010  (b) 1115  
 (c) 1030 (d) 1031 
3.  What is the value of 
1 1 1
...
0.2 0.02 0.002
+ + + upto 
9 terms?  
  
1 1 1
...
0.2 0.02 0.002
+ + + 9 heoeW lekeâ keâe ceeve keäÙee nw?  
 (a) 222222222    (b) 111111111   
 (c) 555555555  (d) 525252525 
4.  What is the value of  
  
3.6 1.62 0.48 3.6
?
1.8 0.8 10.8 0.3 2.16
× + ×
× + × -
  
  
3.6 1.62 0.48 3.6
1.8 0.8 10.8 0.3 2.16
× + ×
× + × -
 keâe ceeve keäÙee nw?  
 (a) 2.4  (b) 2  
 (c) 4 (d) 3 
5.  If 
1 5
= ,
1
8
1+
1
1 +
1
1 +
x
 then what is the value of x?  
  Ùeefo 
1 5
= ,
1
8
1+
1
1 +
1
1 +
x
 nes, lees x keâe ceeve keäÙee nw?    
 (a) 2  (b) 3  
 (c) 1 (d) 4 
6.  If 
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
1 1 1 1 1 1
1+ 1 + 1+ 1+ 1- 1-
2 4 6 8 3 5
? ?
? ?
? ?
1 1
1- = 1+ ,
7 x
 then what is the value of x?   
  Ùeefo 
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
1 1 1 1 1 1
1+ 1 + 1+ 1+ 1- 1-
2 4 6 8 3 5
 
? ?
? ?
? ?
1 1
1- = 1+ ,
7 x
 nes lees  x keâe ceeve keäÙee nw?  
 (a) 6  (b) 8  
 (c) 5 (d) 7 
7.  What is the value of 
  
1 1 1 1
+ + + .... + ?
3×7 7×11 11×15 899×903
  
  
1 1 1 1
+ + + .... +
3×7 7×11 11×15 899×903
 keâe ceeve 
keäÙee nw?  
 (a) 21/500  (b) 18/403  
 (c) 25/301 (d) 29/31 
8.  What is the unit digit of 1
5
+2
5
+3
5
+....+20
5
?  
  1
5
+2
5
+3
5
+....+20
5 
keâe FkeâeF& Debkeâ keäÙee nw?  
 (a) 0  (b) 5  
 (c) 2 (d) 4 
9.  x, y and z are prime numbers and x+y+z = 38. 
What is the maximum value of x?  
  x, y leLee z DeYeepÙe mebKÙeeSB nw leLee   x+y+z = 38 nw~ 
x keâe DeefOekeâlece ceeve keäÙee nw?  
 (a) 19  (b) 23  
 (c) 31 (d) 79 
10.  N is the smallest three digit prime number. 
When N is divided by 13, then what will be the 
reminder?   
  N leerve DebkeâeW keâer meyemes Úesšer DeYeepÙe mebKÙee nw~ peye 
N keâes 13 mes efJeYeeefpele efkeâÙee peelee nw, lees Mes<eheâue 
keäÙee nesiee?  
 (a) 8  (b) 9  
 (c) 7 (d) 10 
11.  How many natural numbers are between 
261 and 45109 ?  
  261 leLee 45109 kesâ ceOÙe efkeâleveer Øeeke=âeflekeâ 
mebKÙeeSB nw? 
 (a) 144  (b) 196  
 (c) 168 (d) 195 
Page 2


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 19-2-2018] [Time : 10 AM to 12 PM 
1.  If N = 1+11+111+1111+ .... + 111111111, then 
what is the some of he digit's of N? 
  Option :  
  Ùeefo N = 1+11+111+1111+ .... + 111111111, nes lees 
N kesâ DebkeâeW keâe Ùeesie keäÙee nw? 
 (a) 45 (b) 18  
 (c) 36 (d) 5 
2.  What is he sum of first 40 terms of 
1+3+4+5+7+7+10+9+ .....?  
  1+3+4+5+7+7+10+9+ ..... kesâ ØeLece 40 heoeW keâe Ùeesie 
keäÙee nw?  
 (a) 1010  (b) 1115  
 (c) 1030 (d) 1031 
3.  What is the value of 
1 1 1
...
0.2 0.02 0.002
+ + + upto 
9 terms?  
  
1 1 1
...
0.2 0.02 0.002
+ + + 9 heoeW lekeâ keâe ceeve keäÙee nw?  
 (a) 222222222    (b) 111111111   
 (c) 555555555  (d) 525252525 
4.  What is the value of  
  
3.6 1.62 0.48 3.6
?
1.8 0.8 10.8 0.3 2.16
× + ×
× + × -
  
  
3.6 1.62 0.48 3.6
1.8 0.8 10.8 0.3 2.16
× + ×
× + × -
 keâe ceeve keäÙee nw?  
 (a) 2.4  (b) 2  
 (c) 4 (d) 3 
5.  If 
1 5
= ,
1
8
1+
1
1 +
1
1 +
x
 then what is the value of x?  
  Ùeefo 
1 5
= ,
1
8
1+
1
1 +
1
1 +
x
 nes, lees x keâe ceeve keäÙee nw?    
 (a) 2  (b) 3  
 (c) 1 (d) 4 
6.  If 
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
1 1 1 1 1 1
1+ 1 + 1+ 1+ 1- 1-
2 4 6 8 3 5
? ?
? ?
? ?
1 1
1- = 1+ ,
7 x
 then what is the value of x?   
  Ùeefo 
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
1 1 1 1 1 1
1+ 1 + 1+ 1+ 1- 1-
2 4 6 8 3 5
 
? ?
? ?
? ?
1 1
1- = 1+ ,
7 x
 nes lees  x keâe ceeve keäÙee nw?  
 (a) 6  (b) 8  
 (c) 5 (d) 7 
7.  What is the value of 
  
1 1 1 1
+ + + .... + ?
3×7 7×11 11×15 899×903
  
  
1 1 1 1
+ + + .... +
3×7 7×11 11×15 899×903
 keâe ceeve 
keäÙee nw?  
 (a) 21/500  (b) 18/403  
 (c) 25/301 (d) 29/31 
8.  What is the unit digit of 1
5
+2
5
+3
5
+....+20
5
?  
  1
5
+2
5
+3
5
+....+20
5 
keâe FkeâeF& Debkeâ keäÙee nw?  
 (a) 0  (b) 5  
 (c) 2 (d) 4 
9.  x, y and z are prime numbers and x+y+z = 38. 
What is the maximum value of x?  
  x, y leLee z DeYeepÙe mebKÙeeSB nw leLee   x+y+z = 38 nw~ 
x keâe DeefOekeâlece ceeve keäÙee nw?  
 (a) 19  (b) 23  
 (c) 31 (d) 79 
10.  N is the smallest three digit prime number. 
When N is divided by 13, then what will be the 
reminder?   
  N leerve DebkeâeW keâer meyemes Úesšer DeYeepÙe mebKÙee nw~ peye 
N keâes 13 mes efJeYeeefpele efkeâÙee peelee nw, lees Mes<eheâue 
keäÙee nesiee?  
 (a) 8  (b) 9  
 (c) 7 (d) 10 
11.  How many natural numbers are between 
261 and 45109 ?  
  261 leLee 45109 kesâ ceOÙe efkeâleveer Øeeke=âeflekeâ 
mebKÙeeSB nw? 
 (a) 144  (b) 196  
 (c) 168 (d) 195 
 
12.  What is the value of  
  121 + 12321 + 1234321 + 123454321 
  121 + 12321 + 1234321 + 123454321 keâe 
ceeve keäÙee nw?  
 (a) 12345  (b) 123456  
 (c) 12344 (d) 123454 
13.  p
3
+q
3
+r
3
 -3pqr = 4. If a =q+r, b=r+p and 
c=p+q, then what is the value of a
3
+b
3
+c
3
 – 
3abc?  
  p
3
+q
3
+r
3
–3pqr = 4 nw~ Ùeefo a =q+r, b=r+p Deewj 
c=p+q nQ, lees a
3
+b
3
+c
3
 – 3abc keâe ceeve keäÙee nw?  
 (a) 4  (b) 8  
 (c) 2 (d) 12 
14.  If a and ß are the roots of the equation x
2
+x-
1=0, then what is the equation whose roots are 
a
5
 and ß
5
?  
  Ùeefo a leLee ß meceerkeâjCe x
2
+x–1=0, kesâ cetue nQ, lees Jen 
meceerkeâjCe keäÙee nw efpemekesâ cetue a
5
 leLee ß
5 
nw? 
 (a) x
2
+7x –1 = 0   (b) x
2
–7x –1 = 0     
 (c) x
2
–11x –1 = 0  (d) x
2
+11x –1 = 0  
15.  If x and y are natural numbers such that x + y 
= 2017, then what is the value of (-1)
x
 + (–1)
y
?  
  Ùeefo x leLee y Øeeke=âeflekeâ mebKÙeeSB Fme Øekeâej nw efkeâ x + 
y = 2017 nw, lees (-1)
x
 + (–1)
y 
keâe ceeve keäÙee nw?  
 (a) 2   (b) –2  
 (c) 0 (d) 1 
16.  If x + (1/x) = ( 3 +1)/2, then what is the value 
of x
4
+(1/x
4
)?  
  Ùeefo x + (1/x) = ( 3 +1)/2 nw, lees x
4
+(1/x
4
)? keâe 
ceeve keäÙee nw?  
 (a) 
( )
4 3 1 / 4 - (b) 
( )
4 3 1 / 2 +  
 (c) 
( )
4 3 1 / 4 - - (d) 
( )
4 3 1 / 2 - -  
17.  If a+a
2
+a
3
-1=0, then what is the value of 
a
3
+(1/a)   
  Ùeefo a+a
2
+a
3
-1=0, nes lees a
3
+(1/a) keâe ceeve keäÙee nw? 
 
 
 (a) 1  (b) 4  
 (c) 2 (d) 3 
18.  If a– (1/a) = b, b – (1/b) = c and c – (1/c) =a, 
then what is the value of (1/ab) + (1/bc) + 
(1/ca)?   
  Ùeefo a– (1/a) = b, b – (1/b) = c leLee c = – (1/c) =a 
nwQ, lees (1/ab) + (1/bc) + (1/ca) keâe ceeve keäÙee nw? 
 (a) –3  (b) –6  
 (c) –1 (d) –9 
19.  If the roots of the equation a(b-c)x
2
+b(c–
a)x+c(a-b)=0 are equal, then which of the 
following is true?     
  Ùeefo meceerkeâjCe a(b-c)x
2
+b(c–a)x+c(a-b)=0 kesâ cetue 
yejeyej nw, lees efvecveefueefKele ceW mes keâewve mee mener nw? 
 (a) b=(a+c)/ac   (b) 2/b=(1/a)+(1/c)  
 (c) 2b = (1/a) + (1/c) (d) abc= ab + bc + ca   
20.  If 
? ?
? ?
2 2
(a + b + ab) +
? ?
? ?
2 2
(a + b - ab) =1, then 
what is the value of (1–a
2
)(1–b
2
)?  
   Ùeefo 
? ?
? ?
2 2
(a + b + ab) +
? ?
? ?
2 2
(a + b - ab) =1, nes 
lees (1–a
2
)(1–b
2
) keâe ceeve keäÙee nw? 
 (a) 1/4 (b) 4/7  
 (c) 5/4 (d) 3/4 
21.  If 3x + 4y –11 = 18 and 8x– 6y + 12 = 6, then 
what is the value of 5x–3y – 9?    
  Ùeefo 3x + 4y –11 = 18 leLee 8x– 6y + 12 = 6 nw, lees 
5x–3y – 9 keâe ceeve keäÙee nw? 
 (a) 18  (b) –9   
 (c) –27 (d) –18   
22.  If a +b+c = 7/12,  3a – 4b + 5c = 3/4 and 7a–11b 
– 13c = –7/12 , then what is the value of a+c?  
  Ùeefo a +b+c = 7/12,  3a – 4b + 5c = 3/4 leLee 7a–
11b – 13c = –7/12  nQ, lees a+c keâe ceeve keäÙee nw? 
 (a) 1/2   (b) 5/12  
 (c) 3/4  (d) 1/4 
23.  The given figure, PQ = PS = SR and 
?QPS=40
0
, then what is the value of ?QPR (in 
degrees)?   
  oer ieF& Deeke=âefle ceW, PQ = PS = SR leLee ?QPS=40
0
, 
nes, lees ?QPR keâe ceeve (ef[«eer ceW) keäÙee nw?   
 
 (a) 45  (b) 60  
 (c) 75 (d) 50 
24.  In triangle PQR, C is the centroid, PQ = 30 cm, 
QR = 36 cm and PR = 50 cm. If D is the 
midpoint of QR, then what is the length (in cm) 
of CD?    
  ef$eYegpe PQR ceW C kesâvõkeâ nw~ PQ = 30 mesceer., QR = 
36 mesceer. leLee PR = 50 mesceer. nw~ Ùeefo D, QR keâe 
ceOÙeefyevog nw, lees CD keâer uecyeeF& (mesceer ceW) keäÙee nw?    
 (a) 
( )
4 86 / 3 (b) 
( )
2 86 / 3  
 (c) 
( )
5 86 /3  (d) 
( )
5 86 / 2  
25.  In the given figure, AQ = 4 2 cm, QC = 6 2 
cm and AB = 20 cm. If PQ is parallel to BC, 
then what is the value ( in cm) of PB?  
  oer ieF& Deeke=âefle ceW AQ = 4 2 mesceer, QC = 6 2 mesceer 
leLee AB = 20 mesceer~ Ùeefo PQ, BC kesâ meceeblej nw, lees 
PB keâe ceeve (mesceer ceW) keäÙee nw?  
 
Page 3


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 19-2-2018] [Time : 10 AM to 12 PM 
1.  If N = 1+11+111+1111+ .... + 111111111, then 
what is the some of he digit's of N? 
  Option :  
  Ùeefo N = 1+11+111+1111+ .... + 111111111, nes lees 
N kesâ DebkeâeW keâe Ùeesie keäÙee nw? 
 (a) 45 (b) 18  
 (c) 36 (d) 5 
2.  What is he sum of first 40 terms of 
1+3+4+5+7+7+10+9+ .....?  
  1+3+4+5+7+7+10+9+ ..... kesâ ØeLece 40 heoeW keâe Ùeesie 
keäÙee nw?  
 (a) 1010  (b) 1115  
 (c) 1030 (d) 1031 
3.  What is the value of 
1 1 1
...
0.2 0.02 0.002
+ + + upto 
9 terms?  
  
1 1 1
...
0.2 0.02 0.002
+ + + 9 heoeW lekeâ keâe ceeve keäÙee nw?  
 (a) 222222222    (b) 111111111   
 (c) 555555555  (d) 525252525 
4.  What is the value of  
  
3.6 1.62 0.48 3.6
?
1.8 0.8 10.8 0.3 2.16
× + ×
× + × -
  
  
3.6 1.62 0.48 3.6
1.8 0.8 10.8 0.3 2.16
× + ×
× + × -
 keâe ceeve keäÙee nw?  
 (a) 2.4  (b) 2  
 (c) 4 (d) 3 
5.  If 
1 5
= ,
1
8
1+
1
1 +
1
1 +
x
 then what is the value of x?  
  Ùeefo 
1 5
= ,
1
8
1+
1
1 +
1
1 +
x
 nes, lees x keâe ceeve keäÙee nw?    
 (a) 2  (b) 3  
 (c) 1 (d) 4 
6.  If 
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
1 1 1 1 1 1
1+ 1 + 1+ 1+ 1- 1-
2 4 6 8 3 5
? ?
? ?
? ?
1 1
1- = 1+ ,
7 x
 then what is the value of x?   
  Ùeefo 
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
1 1 1 1 1 1
1+ 1 + 1+ 1+ 1- 1-
2 4 6 8 3 5
 
? ?
? ?
? ?
1 1
1- = 1+ ,
7 x
 nes lees  x keâe ceeve keäÙee nw?  
 (a) 6  (b) 8  
 (c) 5 (d) 7 
7.  What is the value of 
  
1 1 1 1
+ + + .... + ?
3×7 7×11 11×15 899×903
  
  
1 1 1 1
+ + + .... +
3×7 7×11 11×15 899×903
 keâe ceeve 
keäÙee nw?  
 (a) 21/500  (b) 18/403  
 (c) 25/301 (d) 29/31 
8.  What is the unit digit of 1
5
+2
5
+3
5
+....+20
5
?  
  1
5
+2
5
+3
5
+....+20
5 
keâe FkeâeF& Debkeâ keäÙee nw?  
 (a) 0  (b) 5  
 (c) 2 (d) 4 
9.  x, y and z are prime numbers and x+y+z = 38. 
What is the maximum value of x?  
  x, y leLee z DeYeepÙe mebKÙeeSB nw leLee   x+y+z = 38 nw~ 
x keâe DeefOekeâlece ceeve keäÙee nw?  
 (a) 19  (b) 23  
 (c) 31 (d) 79 
10.  N is the smallest three digit prime number. 
When N is divided by 13, then what will be the 
reminder?   
  N leerve DebkeâeW keâer meyemes Úesšer DeYeepÙe mebKÙee nw~ peye 
N keâes 13 mes efJeYeeefpele efkeâÙee peelee nw, lees Mes<eheâue 
keäÙee nesiee?  
 (a) 8  (b) 9  
 (c) 7 (d) 10 
11.  How many natural numbers are between 
261 and 45109 ?  
  261 leLee 45109 kesâ ceOÙe efkeâleveer Øeeke=âeflekeâ 
mebKÙeeSB nw? 
 (a) 144  (b) 196  
 (c) 168 (d) 195 
 
12.  What is the value of  
  121 + 12321 + 1234321 + 123454321 
  121 + 12321 + 1234321 + 123454321 keâe 
ceeve keäÙee nw?  
 (a) 12345  (b) 123456  
 (c) 12344 (d) 123454 
13.  p
3
+q
3
+r
3
 -3pqr = 4. If a =q+r, b=r+p and 
c=p+q, then what is the value of a
3
+b
3
+c
3
 – 
3abc?  
  p
3
+q
3
+r
3
–3pqr = 4 nw~ Ùeefo a =q+r, b=r+p Deewj 
c=p+q nQ, lees a
3
+b
3
+c
3
 – 3abc keâe ceeve keäÙee nw?  
 (a) 4  (b) 8  
 (c) 2 (d) 12 
14.  If a and ß are the roots of the equation x
2
+x-
1=0, then what is the equation whose roots are 
a
5
 and ß
5
?  
  Ùeefo a leLee ß meceerkeâjCe x
2
+x–1=0, kesâ cetue nQ, lees Jen 
meceerkeâjCe keäÙee nw efpemekesâ cetue a
5
 leLee ß
5 
nw? 
 (a) x
2
+7x –1 = 0   (b) x
2
–7x –1 = 0     
 (c) x
2
–11x –1 = 0  (d) x
2
+11x –1 = 0  
15.  If x and y are natural numbers such that x + y 
= 2017, then what is the value of (-1)
x
 + (–1)
y
?  
  Ùeefo x leLee y Øeeke=âeflekeâ mebKÙeeSB Fme Øekeâej nw efkeâ x + 
y = 2017 nw, lees (-1)
x
 + (–1)
y 
keâe ceeve keäÙee nw?  
 (a) 2   (b) –2  
 (c) 0 (d) 1 
16.  If x + (1/x) = ( 3 +1)/2, then what is the value 
of x
4
+(1/x
4
)?  
  Ùeefo x + (1/x) = ( 3 +1)/2 nw, lees x
4
+(1/x
4
)? keâe 
ceeve keäÙee nw?  
 (a) 
( )
4 3 1 / 4 - (b) 
( )
4 3 1 / 2 +  
 (c) 
( )
4 3 1 / 4 - - (d) 
( )
4 3 1 / 2 - -  
17.  If a+a
2
+a
3
-1=0, then what is the value of 
a
3
+(1/a)   
  Ùeefo a+a
2
+a
3
-1=0, nes lees a
3
+(1/a) keâe ceeve keäÙee nw? 
 
 
 (a) 1  (b) 4  
 (c) 2 (d) 3 
18.  If a– (1/a) = b, b – (1/b) = c and c – (1/c) =a, 
then what is the value of (1/ab) + (1/bc) + 
(1/ca)?   
  Ùeefo a– (1/a) = b, b – (1/b) = c leLee c = – (1/c) =a 
nwQ, lees (1/ab) + (1/bc) + (1/ca) keâe ceeve keäÙee nw? 
 (a) –3  (b) –6  
 (c) –1 (d) –9 
19.  If the roots of the equation a(b-c)x
2
+b(c–
a)x+c(a-b)=0 are equal, then which of the 
following is true?     
  Ùeefo meceerkeâjCe a(b-c)x
2
+b(c–a)x+c(a-b)=0 kesâ cetue 
yejeyej nw, lees efvecveefueefKele ceW mes keâewve mee mener nw? 
 (a) b=(a+c)/ac   (b) 2/b=(1/a)+(1/c)  
 (c) 2b = (1/a) + (1/c) (d) abc= ab + bc + ca   
20.  If 
? ?
? ?
2 2
(a + b + ab) +
? ?
? ?
2 2
(a + b - ab) =1, then 
what is the value of (1–a
2
)(1–b
2
)?  
   Ùeefo 
? ?
? ?
2 2
(a + b + ab) +
? ?
? ?
2 2
(a + b - ab) =1, nes 
lees (1–a
2
)(1–b
2
) keâe ceeve keäÙee nw? 
 (a) 1/4 (b) 4/7  
 (c) 5/4 (d) 3/4 
21.  If 3x + 4y –11 = 18 and 8x– 6y + 12 = 6, then 
what is the value of 5x–3y – 9?    
  Ùeefo 3x + 4y –11 = 18 leLee 8x– 6y + 12 = 6 nw, lees 
5x–3y – 9 keâe ceeve keäÙee nw? 
 (a) 18  (b) –9   
 (c) –27 (d) –18   
22.  If a +b+c = 7/12,  3a – 4b + 5c = 3/4 and 7a–11b 
– 13c = –7/12 , then what is the value of a+c?  
  Ùeefo a +b+c = 7/12,  3a – 4b + 5c = 3/4 leLee 7a–
11b – 13c = –7/12  nQ, lees a+c keâe ceeve keäÙee nw? 
 (a) 1/2   (b) 5/12  
 (c) 3/4  (d) 1/4 
23.  The given figure, PQ = PS = SR and 
?QPS=40
0
, then what is the value of ?QPR (in 
degrees)?   
  oer ieF& Deeke=âefle ceW, PQ = PS = SR leLee ?QPS=40
0
, 
nes, lees ?QPR keâe ceeve (ef[«eer ceW) keäÙee nw?   
 
 (a) 45  (b) 60  
 (c) 75 (d) 50 
24.  In triangle PQR, C is the centroid, PQ = 30 cm, 
QR = 36 cm and PR = 50 cm. If D is the 
midpoint of QR, then what is the length (in cm) 
of CD?    
  ef$eYegpe PQR ceW C kesâvõkeâ nw~ PQ = 30 mesceer., QR = 
36 mesceer. leLee PR = 50 mesceer. nw~ Ùeefo D, QR keâe 
ceOÙeefyevog nw, lees CD keâer uecyeeF& (mesceer ceW) keäÙee nw?    
 (a) 
( )
4 86 / 3 (b) 
( )
2 86 / 3  
 (c) 
( )
5 86 /3  (d) 
( )
5 86 / 2  
25.  In the given figure, AQ = 4 2 cm, QC = 6 2 
cm and AB = 20 cm. If PQ is parallel to BC, 
then what is the value ( in cm) of PB?  
  oer ieF& Deeke=âefle ceW AQ = 4 2 mesceer, QC = 6 2 mesceer 
leLee AB = 20 mesceer~ Ùeefo PQ, BC kesâ meceeblej nw, lees 
PB keâe ceeve (mesceer ceW) keäÙee nw?  
 
 
 (a) 8  (b) 12  
 (c) 6 (d) 15 
26.  In the given figure, if AD = 12 cm, AE = 8cm 
and EC = 14 cm, then what is the value (in cm) 
of BD?  
  oer ieF& Deeke=âefle ceW AD = 12 mesceer., AE = 8 mesceer leLee 
EC = 14 mesceer nQ, lees BD keâe ceeve (mesceer ceW) keäÙee nw? 
 
 (a) 50/3  (b) 15  
 (c) 8/3 (d) 44/3 
27.  Two circle are having radii 9 cm and 12 cm. 
The distance between their centres is 15cm. 
What is the length (in cm) of their common 
chord?/oes Je=òeeW keâer ef$epÙeeSB 9 mesceer. leLee 12 mesceer nQ~ 
oesveeW kesâ kesâõeW kesâ ceOÙe keâer otjer 15 mesceer nw~ Gvekeâer 
meeceevÙe peerJee keâer uecyeeF& (mesceer. ceW) keäÙee nw?  
 (a) 6.8  (b) 13.6  
 (c) 7.2 (d) 14.4 
28.  Two circle touch each other at point X. Two 
common tangents of the circle meet at point P 
and none of the tangents passes through X. 
These tangents touch the larger circle at points 
B and C. If the radius of the larger circle is 15 
cm and CP = 20 cm, then what is the radius (in 
cm) of the smaller circle?     
  oes Je=òe efyebog X hej Skeâ otmejs keâes mheMe& keâjles nQ~ Je=òeeW 
keâer oes meceeve mheMe&jsKeeSB efyebog P hej efceueleer nw leLee 
keâesF& Yeer mheMe& jsKee X mes veneR iegpejleer nw~ Ùen 
mheMe&jsKeeSb yeÌ[s Je=òe keâes efyebog B leLee C hej mheMe& keâjleer 
nw~ Ùeefo yeÌ[s Je=òe keâer ef$epÙee 15 mesceer leLee  CP = 20 
mesceer nw, lees Úesšs Je=òe keâer ef$epÙee (mesceer ceW) keäÙee nw? 
 (a) 3.5  (b) 3.75  
 (c) 4.25 (d) 4.45 
29.  Two circles touch each other of point X. A 
common tangent touch them at two distinct 
points Y and Z. If another tangent passing 
through X cut YZ at A and XA = 16 cm, then 
what is the vale (in cm) of YZ?    
  oes Je=òe Skeâ -otmejs keâes efyebog X hej mheMe& keâjles nQ~ Skeâ 
meceeve mheMe&jsKee GvnW oes Deueie efyebogDeeW Y leLee Z hej 
mheMe& keâjleer nw~ Ùeefo X mes iegpejves Jeeueer Skeâ DevÙe 
mheMe&jsKee YZ keâes A hej keâešleer nw leLee XA = 16 mesceer 
nw, YZ keâe ceeve (mesceer. ceW) keäÙee nw?  
 (a) 18  (b) 24  
 (c) 16 (d) 32 
30.  There are 8 equidistant points A, B, C, D, E, F, 
G and H (in same order) on a circle. What is 
the value of ?FDH (in degree)?   
  Skeâ Je=òe hej 8 meceeveeblej efyebog A, B, C, D, E, F, G 
leLee H (Fmeer ›eâce ceW) nQ~ ?FDH keâe ceeve (ef[«eer ceW) 
keäÙee nw? 
 (a) 22.5  (b) 45  
 (c) 30 (d) 42.5 
31.  In the Given the figure, O is the centre of the 
circle and ?QOR = 50
0
, then what is the value 
of ?RPQ (in degrees)?  
  oer ieF& Deeke=âefle ceW O Skeâ Je=òe keâe kesâõ nw leLee ?QOR 
= 50
0 
nw, lees ?RPQ keâe ceeve (ef[«eer ceW) keäÙee nw?   
 
 (a) 15  (b) 25  
 (c) 20 (d) 30 
32.  Three circle C
1
, C
2
 and C
3
 with radii r
1
, r
2
 and 
r
3
 (where r
1
 < r
2
 < r
3
) are placed as shown in 
the given figure. What is the value of r
2
?    
  leerve Je=òe C
1
, C
2
 leLee C
3
 efpevekeâer ef$epÙeeSB r
1
, r
2
 leLee 
r
3
 (peneB r
1
 < r
2
 < r
3
) keâes oer ngF& Deeke=âefle ceW oMee&Ùee 
ieÙee nw~ r
2 
keâe ceeve keäÙee nw? 
 
 (a) ( )
1 3
r r  (b) ( )
1 3
r r / 2 +  
 (c) ( ) ( )
1 2 1 2
2r r / r r + (d) ( )
1 3
r r + 
33.  An equilateral triangle of area 300 cm
2
 is cut 
from its three vertices to form a regular 
hexagon. Area of hexagon is what percent of 
the area of triangle?    
  Skeâ meceyeeng ef$eYegpe efpemekeâe #es$eheâue 300 mesceer
2
 nw, 
keâes Gmekesâ leerveeW Meer<eeX mes Skeâ mece<ešYegpe yeveeves kesâ 
efueS keâeše peelee nw~ <ešYegpe keâe #es$eheâue ef$eYegpe kesâ 
#es$eheâue keâe efkeâlevee ØeefleMele nw?   
 (a) 66.66%  (b) 33.33%  
 (c) 83.33% (d) 56.41% 
34.  In the given figure, PQR is an equilateral 
triangle with side as 12 cm. S and T are the mid 
points of the sides PQ and PR respectively. 
What is the area (in cm
2
) of the shaded region?   
  oer ieF& Deeke=âefle ceW, PQR Skeâ meceyeeng ef$eYegpe nw, 
efpemekeâer Yegpee 12 mesceer nw~ S leLee T, ›eâceMe: Yegpee PQ  
leLee PR kesâ ceOÙe efyevog nw~ ÚeÙeebefkeâle Yeeie keâe #es$eheâue 
(mesceer
2
 ceW) keäÙee nw?   
 
Page 4


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 19-2-2018] [Time : 10 AM to 12 PM 
1.  If N = 1+11+111+1111+ .... + 111111111, then 
what is the some of he digit's of N? 
  Option :  
  Ùeefo N = 1+11+111+1111+ .... + 111111111, nes lees 
N kesâ DebkeâeW keâe Ùeesie keäÙee nw? 
 (a) 45 (b) 18  
 (c) 36 (d) 5 
2.  What is he sum of first 40 terms of 
1+3+4+5+7+7+10+9+ .....?  
  1+3+4+5+7+7+10+9+ ..... kesâ ØeLece 40 heoeW keâe Ùeesie 
keäÙee nw?  
 (a) 1010  (b) 1115  
 (c) 1030 (d) 1031 
3.  What is the value of 
1 1 1
...
0.2 0.02 0.002
+ + + upto 
9 terms?  
  
1 1 1
...
0.2 0.02 0.002
+ + + 9 heoeW lekeâ keâe ceeve keäÙee nw?  
 (a) 222222222    (b) 111111111   
 (c) 555555555  (d) 525252525 
4.  What is the value of  
  
3.6 1.62 0.48 3.6
?
1.8 0.8 10.8 0.3 2.16
× + ×
× + × -
  
  
3.6 1.62 0.48 3.6
1.8 0.8 10.8 0.3 2.16
× + ×
× + × -
 keâe ceeve keäÙee nw?  
 (a) 2.4  (b) 2  
 (c) 4 (d) 3 
5.  If 
1 5
= ,
1
8
1+
1
1 +
1
1 +
x
 then what is the value of x?  
  Ùeefo 
1 5
= ,
1
8
1+
1
1 +
1
1 +
x
 nes, lees x keâe ceeve keäÙee nw?    
 (a) 2  (b) 3  
 (c) 1 (d) 4 
6.  If 
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
1 1 1 1 1 1
1+ 1 + 1+ 1+ 1- 1-
2 4 6 8 3 5
? ?
? ?
? ?
1 1
1- = 1+ ,
7 x
 then what is the value of x?   
  Ùeefo 
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
1 1 1 1 1 1
1+ 1 + 1+ 1+ 1- 1-
2 4 6 8 3 5
 
? ?
? ?
? ?
1 1
1- = 1+ ,
7 x
 nes lees  x keâe ceeve keäÙee nw?  
 (a) 6  (b) 8  
 (c) 5 (d) 7 
7.  What is the value of 
  
1 1 1 1
+ + + .... + ?
3×7 7×11 11×15 899×903
  
  
1 1 1 1
+ + + .... +
3×7 7×11 11×15 899×903
 keâe ceeve 
keäÙee nw?  
 (a) 21/500  (b) 18/403  
 (c) 25/301 (d) 29/31 
8.  What is the unit digit of 1
5
+2
5
+3
5
+....+20
5
?  
  1
5
+2
5
+3
5
+....+20
5 
keâe FkeâeF& Debkeâ keäÙee nw?  
 (a) 0  (b) 5  
 (c) 2 (d) 4 
9.  x, y and z are prime numbers and x+y+z = 38. 
What is the maximum value of x?  
  x, y leLee z DeYeepÙe mebKÙeeSB nw leLee   x+y+z = 38 nw~ 
x keâe DeefOekeâlece ceeve keäÙee nw?  
 (a) 19  (b) 23  
 (c) 31 (d) 79 
10.  N is the smallest three digit prime number. 
When N is divided by 13, then what will be the 
reminder?   
  N leerve DebkeâeW keâer meyemes Úesšer DeYeepÙe mebKÙee nw~ peye 
N keâes 13 mes efJeYeeefpele efkeâÙee peelee nw, lees Mes<eheâue 
keäÙee nesiee?  
 (a) 8  (b) 9  
 (c) 7 (d) 10 
11.  How many natural numbers are between 
261 and 45109 ?  
  261 leLee 45109 kesâ ceOÙe efkeâleveer Øeeke=âeflekeâ 
mebKÙeeSB nw? 
 (a) 144  (b) 196  
 (c) 168 (d) 195 
 
12.  What is the value of  
  121 + 12321 + 1234321 + 123454321 
  121 + 12321 + 1234321 + 123454321 keâe 
ceeve keäÙee nw?  
 (a) 12345  (b) 123456  
 (c) 12344 (d) 123454 
13.  p
3
+q
3
+r
3
 -3pqr = 4. If a =q+r, b=r+p and 
c=p+q, then what is the value of a
3
+b
3
+c
3
 – 
3abc?  
  p
3
+q
3
+r
3
–3pqr = 4 nw~ Ùeefo a =q+r, b=r+p Deewj 
c=p+q nQ, lees a
3
+b
3
+c
3
 – 3abc keâe ceeve keäÙee nw?  
 (a) 4  (b) 8  
 (c) 2 (d) 12 
14.  If a and ß are the roots of the equation x
2
+x-
1=0, then what is the equation whose roots are 
a
5
 and ß
5
?  
  Ùeefo a leLee ß meceerkeâjCe x
2
+x–1=0, kesâ cetue nQ, lees Jen 
meceerkeâjCe keäÙee nw efpemekesâ cetue a
5
 leLee ß
5 
nw? 
 (a) x
2
+7x –1 = 0   (b) x
2
–7x –1 = 0     
 (c) x
2
–11x –1 = 0  (d) x
2
+11x –1 = 0  
15.  If x and y are natural numbers such that x + y 
= 2017, then what is the value of (-1)
x
 + (–1)
y
?  
  Ùeefo x leLee y Øeeke=âeflekeâ mebKÙeeSB Fme Øekeâej nw efkeâ x + 
y = 2017 nw, lees (-1)
x
 + (–1)
y 
keâe ceeve keäÙee nw?  
 (a) 2   (b) –2  
 (c) 0 (d) 1 
16.  If x + (1/x) = ( 3 +1)/2, then what is the value 
of x
4
+(1/x
4
)?  
  Ùeefo x + (1/x) = ( 3 +1)/2 nw, lees x
4
+(1/x
4
)? keâe 
ceeve keäÙee nw?  
 (a) 
( )
4 3 1 / 4 - (b) 
( )
4 3 1 / 2 +  
 (c) 
( )
4 3 1 / 4 - - (d) 
( )
4 3 1 / 2 - -  
17.  If a+a
2
+a
3
-1=0, then what is the value of 
a
3
+(1/a)   
  Ùeefo a+a
2
+a
3
-1=0, nes lees a
3
+(1/a) keâe ceeve keäÙee nw? 
 
 
 (a) 1  (b) 4  
 (c) 2 (d) 3 
18.  If a– (1/a) = b, b – (1/b) = c and c – (1/c) =a, 
then what is the value of (1/ab) + (1/bc) + 
(1/ca)?   
  Ùeefo a– (1/a) = b, b – (1/b) = c leLee c = – (1/c) =a 
nwQ, lees (1/ab) + (1/bc) + (1/ca) keâe ceeve keäÙee nw? 
 (a) –3  (b) –6  
 (c) –1 (d) –9 
19.  If the roots of the equation a(b-c)x
2
+b(c–
a)x+c(a-b)=0 are equal, then which of the 
following is true?     
  Ùeefo meceerkeâjCe a(b-c)x
2
+b(c–a)x+c(a-b)=0 kesâ cetue 
yejeyej nw, lees efvecveefueefKele ceW mes keâewve mee mener nw? 
 (a) b=(a+c)/ac   (b) 2/b=(1/a)+(1/c)  
 (c) 2b = (1/a) + (1/c) (d) abc= ab + bc + ca   
20.  If 
? ?
? ?
2 2
(a + b + ab) +
? ?
? ?
2 2
(a + b - ab) =1, then 
what is the value of (1–a
2
)(1–b
2
)?  
   Ùeefo 
? ?
? ?
2 2
(a + b + ab) +
? ?
? ?
2 2
(a + b - ab) =1, nes 
lees (1–a
2
)(1–b
2
) keâe ceeve keäÙee nw? 
 (a) 1/4 (b) 4/7  
 (c) 5/4 (d) 3/4 
21.  If 3x + 4y –11 = 18 and 8x– 6y + 12 = 6, then 
what is the value of 5x–3y – 9?    
  Ùeefo 3x + 4y –11 = 18 leLee 8x– 6y + 12 = 6 nw, lees 
5x–3y – 9 keâe ceeve keäÙee nw? 
 (a) 18  (b) –9   
 (c) –27 (d) –18   
22.  If a +b+c = 7/12,  3a – 4b + 5c = 3/4 and 7a–11b 
– 13c = –7/12 , then what is the value of a+c?  
  Ùeefo a +b+c = 7/12,  3a – 4b + 5c = 3/4 leLee 7a–
11b – 13c = –7/12  nQ, lees a+c keâe ceeve keäÙee nw? 
 (a) 1/2   (b) 5/12  
 (c) 3/4  (d) 1/4 
23.  The given figure, PQ = PS = SR and 
?QPS=40
0
, then what is the value of ?QPR (in 
degrees)?   
  oer ieF& Deeke=âefle ceW, PQ = PS = SR leLee ?QPS=40
0
, 
nes, lees ?QPR keâe ceeve (ef[«eer ceW) keäÙee nw?   
 
 (a) 45  (b) 60  
 (c) 75 (d) 50 
24.  In triangle PQR, C is the centroid, PQ = 30 cm, 
QR = 36 cm and PR = 50 cm. If D is the 
midpoint of QR, then what is the length (in cm) 
of CD?    
  ef$eYegpe PQR ceW C kesâvõkeâ nw~ PQ = 30 mesceer., QR = 
36 mesceer. leLee PR = 50 mesceer. nw~ Ùeefo D, QR keâe 
ceOÙeefyevog nw, lees CD keâer uecyeeF& (mesceer ceW) keäÙee nw?    
 (a) 
( )
4 86 / 3 (b) 
( )
2 86 / 3  
 (c) 
( )
5 86 /3  (d) 
( )
5 86 / 2  
25.  In the given figure, AQ = 4 2 cm, QC = 6 2 
cm and AB = 20 cm. If PQ is parallel to BC, 
then what is the value ( in cm) of PB?  
  oer ieF& Deeke=âefle ceW AQ = 4 2 mesceer, QC = 6 2 mesceer 
leLee AB = 20 mesceer~ Ùeefo PQ, BC kesâ meceeblej nw, lees 
PB keâe ceeve (mesceer ceW) keäÙee nw?  
 
 
 (a) 8  (b) 12  
 (c) 6 (d) 15 
26.  In the given figure, if AD = 12 cm, AE = 8cm 
and EC = 14 cm, then what is the value (in cm) 
of BD?  
  oer ieF& Deeke=âefle ceW AD = 12 mesceer., AE = 8 mesceer leLee 
EC = 14 mesceer nQ, lees BD keâe ceeve (mesceer ceW) keäÙee nw? 
 
 (a) 50/3  (b) 15  
 (c) 8/3 (d) 44/3 
27.  Two circle are having radii 9 cm and 12 cm. 
The distance between their centres is 15cm. 
What is the length (in cm) of their common 
chord?/oes Je=òeeW keâer ef$epÙeeSB 9 mesceer. leLee 12 mesceer nQ~ 
oesveeW kesâ kesâõeW kesâ ceOÙe keâer otjer 15 mesceer nw~ Gvekeâer 
meeceevÙe peerJee keâer uecyeeF& (mesceer. ceW) keäÙee nw?  
 (a) 6.8  (b) 13.6  
 (c) 7.2 (d) 14.4 
28.  Two circle touch each other at point X. Two 
common tangents of the circle meet at point P 
and none of the tangents passes through X. 
These tangents touch the larger circle at points 
B and C. If the radius of the larger circle is 15 
cm and CP = 20 cm, then what is the radius (in 
cm) of the smaller circle?     
  oes Je=òe efyebog X hej Skeâ otmejs keâes mheMe& keâjles nQ~ Je=òeeW 
keâer oes meceeve mheMe&jsKeeSB efyebog P hej efceueleer nw leLee 
keâesF& Yeer mheMe& jsKee X mes veneR iegpejleer nw~ Ùen 
mheMe&jsKeeSb yeÌ[s Je=òe keâes efyebog B leLee C hej mheMe& keâjleer 
nw~ Ùeefo yeÌ[s Je=òe keâer ef$epÙee 15 mesceer leLee  CP = 20 
mesceer nw, lees Úesšs Je=òe keâer ef$epÙee (mesceer ceW) keäÙee nw? 
 (a) 3.5  (b) 3.75  
 (c) 4.25 (d) 4.45 
29.  Two circles touch each other of point X. A 
common tangent touch them at two distinct 
points Y and Z. If another tangent passing 
through X cut YZ at A and XA = 16 cm, then 
what is the vale (in cm) of YZ?    
  oes Je=òe Skeâ -otmejs keâes efyebog X hej mheMe& keâjles nQ~ Skeâ 
meceeve mheMe&jsKee GvnW oes Deueie efyebogDeeW Y leLee Z hej 
mheMe& keâjleer nw~ Ùeefo X mes iegpejves Jeeueer Skeâ DevÙe 
mheMe&jsKee YZ keâes A hej keâešleer nw leLee XA = 16 mesceer 
nw, YZ keâe ceeve (mesceer. ceW) keäÙee nw?  
 (a) 18  (b) 24  
 (c) 16 (d) 32 
30.  There are 8 equidistant points A, B, C, D, E, F, 
G and H (in same order) on a circle. What is 
the value of ?FDH (in degree)?   
  Skeâ Je=òe hej 8 meceeveeblej efyebog A, B, C, D, E, F, G 
leLee H (Fmeer ›eâce ceW) nQ~ ?FDH keâe ceeve (ef[«eer ceW) 
keäÙee nw? 
 (a) 22.5  (b) 45  
 (c) 30 (d) 42.5 
31.  In the Given the figure, O is the centre of the 
circle and ?QOR = 50
0
, then what is the value 
of ?RPQ (in degrees)?  
  oer ieF& Deeke=âefle ceW O Skeâ Je=òe keâe kesâõ nw leLee ?QOR 
= 50
0 
nw, lees ?RPQ keâe ceeve (ef[«eer ceW) keäÙee nw?   
 
 (a) 15  (b) 25  
 (c) 20 (d) 30 
32.  Three circle C
1
, C
2
 and C
3
 with radii r
1
, r
2
 and 
r
3
 (where r
1
 < r
2
 < r
3
) are placed as shown in 
the given figure. What is the value of r
2
?    
  leerve Je=òe C
1
, C
2
 leLee C
3
 efpevekeâer ef$epÙeeSB r
1
, r
2
 leLee 
r
3
 (peneB r
1
 < r
2
 < r
3
) keâes oer ngF& Deeke=âefle ceW oMee&Ùee 
ieÙee nw~ r
2 
keâe ceeve keäÙee nw? 
 
 (a) ( )
1 3
r r  (b) ( )
1 3
r r / 2 +  
 (c) ( ) ( )
1 2 1 2
2r r / r r + (d) ( )
1 3
r r + 
33.  An equilateral triangle of area 300 cm
2
 is cut 
from its three vertices to form a regular 
hexagon. Area of hexagon is what percent of 
the area of triangle?    
  Skeâ meceyeeng ef$eYegpe efpemekeâe #es$eheâue 300 mesceer
2
 nw, 
keâes Gmekesâ leerveeW Meer<eeX mes Skeâ mece<ešYegpe yeveeves kesâ 
efueS keâeše peelee nw~ <ešYegpe keâe #es$eheâue ef$eYegpe kesâ 
#es$eheâue keâe efkeâlevee ØeefleMele nw?   
 (a) 66.66%  (b) 33.33%  
 (c) 83.33% (d) 56.41% 
34.  In the given figure, PQR is an equilateral 
triangle with side as 12 cm. S and T are the mid 
points of the sides PQ and PR respectively. 
What is the area (in cm
2
) of the shaded region?   
  oer ieF& Deeke=âefle ceW, PQR Skeâ meceyeeng ef$eYegpe nw, 
efpemekeâer Yegpee 12 mesceer nw~ S leLee T, ›eâceMe: Yegpee PQ  
leLee PR kesâ ceOÙe efyevog nw~ ÚeÙeebefkeâle Yeeie keâe #es$eheâue 
(mesceer
2
 ceW) keäÙee nw?   
 
 
 (a) 10 3  (b) 12 3  
 (c) 9 3 (d) 14 3 
35.  ABCD is a rectangle. P is a point on the side 
AB as shown in the given figure. If DP = 13. CP 
= 10 and BP = 6, then what is the value of AP?     
  ABCD Skeâ DeeÙele nw~ P, Yegpee AB hej Skeâ efyevog nw, 
pewmee efkeâ oer ieF& Deeke=âefle ceW oMee&Ùee ieÙee nw~ DP = 13. 
CP = 10 Deewj BP = 6 nes, lees  AP keâe ceeve keäÙee nw?  
 
 (a) 105  (b) 133  
 (c) 12 (d) 10 
36.  In the given figure, PQRSTU is a regular 
hexagon of side 12 cm. what is the area (in cm
2
) 
of triangle SQU?  
  oer ieF& Deeke=âefle ceW PQRSTU Skeâ mece<ešYegpe nw 
efpemekeâer Yegpee 12 mesceer. nw~ ef$eYegpe SQU keâe #es$eheâue 
(mesceer
2
ceW) keäÙee nw?  
 
 (a) 162 3 (b) 216 3 
 (c) 108 3  (d) 54 3 
37.  In the given figure, ABCD is a square, BCXYZ 
is a regular pentagon and ABE is an equilateral 
triangle. What is the value ( in degrees) of 
?EBZ?   
  oer ieF& Deeke=âefle cessb, ABCD keâe Jeie& nw, BCXYZ Skeâ 
mece hebÛeYegpe nw leLee ABE Skeâ meceef$eYegpe nw ?EBZ 
keâe ceeve (ef[«eer ceW) keäÙee nw? 
 
 (a) 102  (b) 98  
 (c) 78 (d) 64 
38.  In the given figure, 3 semicircles are drawn on 
three sides of triangle ABC. AB = 21 cm. BC = 
28 cm and AC = 35 cm. What is the area (in 
cm
2
) of the shaded part?  
  oer ieF& Deeke=âefle ceW, ef$eYegpe ABC keâer leerveeW YegpeeDeeW hej 
3 DeOe&Je=òe yeveeÙes ieÙes nQ~ AB = 21 mesceer, BC = 28 
mesceer leLee AC = 35 mesceer~ ÚeÙeebefkeâle Yeeie keâe #es$eheâue 
(mesceer ceW) keäÙee nQ?   
 
 (a) 588  (b) 324  
 (c) 294 (d) 286 
39.  The sum of radii of the two circle is 91 cm and 
the difference between their area in 2002 cm
2
. 
What is the radius (in cm) of the larger circle?   
  oes Je=òeeW keâer ef$epÙeeDeeW keâe Ùeesie 91 mesceer nw leLee Gvekesâ 
#es$eheâue kesâ ceOÙe keâe Deblej 2002 mesceer
2
 nw~ yeÌ[s Je=òe keâer 
ef$epÙee (mesceer ceW) keäÙee nw?   
 (a) 56  (b) 42  
 (c) 63 (d) 49 
40.  A right triangular prism has equilateral 
triangle as its base. Side of the triangle is 15 
cm. Hight of the prism is 20 3 cm. What is the 
volume (in cm
3
) of the?   
  Skeâ uecyeJele ef$eYegpeekeâej efØep]ce keâe DeeOeej meceyeeng 
ef$eYegpe keâer Yegpee 15 mesceer. nw~ efØep]ce keâer TBÛeeF& 
20 3 mesceer. nw~ efØep]ce keâe DeeÙeleve (mesceer.
3
 ceW) keäÙee nw?   
 (a) 1125  (b) 6750  
 (c) 4500 (d) 3375 
41.  The higher of a cone is 45 cm. It is cut at a 
height of 15 cm from its base by a plane 
parallel to its base. If the volume of the smaller 
cone is 18480 cm
3
, then what is the volume (in 
cm
3
) of the original cone?  
  Skeâ Mebkegâ keâer GBâÛeeF& 45 mesceer. nw~ Fmes DeeOeej mes 15 
mesceer Thej Skeâ leue Éeje Gmekesâ DeeOeej kesâ meceeveeblej 
keâeše peelee nw~ Ùeefo Úesšs Mebkegâ keâe DeeÙeleve 18480 
mesceer
3
 nw, lees cetue Mebkegâ keâe DeeÙeleve (mesceer.
3 
ceW) keäÙee nw?  
 (a) 34650  (b) 61600   
 (c) 36960 (d) 62370 
42.  The radio of the curved surface area and total 
surface area of a right circular cylinder is 2:5. 
If the total surface area is 3080 cm
2
, then what 
is the volume (in cm
3
) of the cylinder?     
  Skeâ uecyeJele Je=òeekeâej yesueve kesâ Je›eâ he=<"erÙe #es$eheâue 
leLee kegâue he=<"erÙe #es$eheâue keâe Devegheele 2 : 5 nQ~ Ùeefo 
kegâue he=<"erÙe #es$eheâue 3080 mesceer
2
 nw, lees yesueve keâe 
DeeÙeleve (mesceer
3
 ceW) keäÙee nw?  
 (a) 4312 6  (b) 3822 6  
 (c) 4522 6 (d) 4642 6 
43.  The radius and height of a solid cylinder are 
increased by 2% each. What will be the 
approximate percentage increase in volume?  
  Skeâ "esme yesueve keâer ef$epÙee leLee GBâÛeeF& ØelÙeskeâ keâes 2³ 
mes yeÌ{eÙee peelee nw~ DeeÙeleve ceW ueieYeie efkeâleves ØeefleMele 
keâer Je=efæ nesieer?  
Page 5


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 19-2-2018] [Time : 10 AM to 12 PM 
1.  If N = 1+11+111+1111+ .... + 111111111, then 
what is the some of he digit's of N? 
  Option :  
  Ùeefo N = 1+11+111+1111+ .... + 111111111, nes lees 
N kesâ DebkeâeW keâe Ùeesie keäÙee nw? 
 (a) 45 (b) 18  
 (c) 36 (d) 5 
2.  What is he sum of first 40 terms of 
1+3+4+5+7+7+10+9+ .....?  
  1+3+4+5+7+7+10+9+ ..... kesâ ØeLece 40 heoeW keâe Ùeesie 
keäÙee nw?  
 (a) 1010  (b) 1115  
 (c) 1030 (d) 1031 
3.  What is the value of 
1 1 1
...
0.2 0.02 0.002
+ + + upto 
9 terms?  
  
1 1 1
...
0.2 0.02 0.002
+ + + 9 heoeW lekeâ keâe ceeve keäÙee nw?  
 (a) 222222222    (b) 111111111   
 (c) 555555555  (d) 525252525 
4.  What is the value of  
  
3.6 1.62 0.48 3.6
?
1.8 0.8 10.8 0.3 2.16
× + ×
× + × -
  
  
3.6 1.62 0.48 3.6
1.8 0.8 10.8 0.3 2.16
× + ×
× + × -
 keâe ceeve keäÙee nw?  
 (a) 2.4  (b) 2  
 (c) 4 (d) 3 
5.  If 
1 5
= ,
1
8
1+
1
1 +
1
1 +
x
 then what is the value of x?  
  Ùeefo 
1 5
= ,
1
8
1+
1
1 +
1
1 +
x
 nes, lees x keâe ceeve keäÙee nw?    
 (a) 2  (b) 3  
 (c) 1 (d) 4 
6.  If 
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
1 1 1 1 1 1
1+ 1 + 1+ 1+ 1- 1-
2 4 6 8 3 5
? ?
? ?
? ?
1 1
1- = 1+ ,
7 x
 then what is the value of x?   
  Ùeefo 
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
? ?? ?? ?? ?? ?? ?
1 1 1 1 1 1
1+ 1 + 1+ 1+ 1- 1-
2 4 6 8 3 5
 
? ?
? ?
? ?
1 1
1- = 1+ ,
7 x
 nes lees  x keâe ceeve keäÙee nw?  
 (a) 6  (b) 8  
 (c) 5 (d) 7 
7.  What is the value of 
  
1 1 1 1
+ + + .... + ?
3×7 7×11 11×15 899×903
  
  
1 1 1 1
+ + + .... +
3×7 7×11 11×15 899×903
 keâe ceeve 
keäÙee nw?  
 (a) 21/500  (b) 18/403  
 (c) 25/301 (d) 29/31 
8.  What is the unit digit of 1
5
+2
5
+3
5
+....+20
5
?  
  1
5
+2
5
+3
5
+....+20
5 
keâe FkeâeF& Debkeâ keäÙee nw?  
 (a) 0  (b) 5  
 (c) 2 (d) 4 
9.  x, y and z are prime numbers and x+y+z = 38. 
What is the maximum value of x?  
  x, y leLee z DeYeepÙe mebKÙeeSB nw leLee   x+y+z = 38 nw~ 
x keâe DeefOekeâlece ceeve keäÙee nw?  
 (a) 19  (b) 23  
 (c) 31 (d) 79 
10.  N is the smallest three digit prime number. 
When N is divided by 13, then what will be the 
reminder?   
  N leerve DebkeâeW keâer meyemes Úesšer DeYeepÙe mebKÙee nw~ peye 
N keâes 13 mes efJeYeeefpele efkeâÙee peelee nw, lees Mes<eheâue 
keäÙee nesiee?  
 (a) 8  (b) 9  
 (c) 7 (d) 10 
11.  How many natural numbers are between 
261 and 45109 ?  
  261 leLee 45109 kesâ ceOÙe efkeâleveer Øeeke=âeflekeâ 
mebKÙeeSB nw? 
 (a) 144  (b) 196  
 (c) 168 (d) 195 
 
12.  What is the value of  
  121 + 12321 + 1234321 + 123454321 
  121 + 12321 + 1234321 + 123454321 keâe 
ceeve keäÙee nw?  
 (a) 12345  (b) 123456  
 (c) 12344 (d) 123454 
13.  p
3
+q
3
+r
3
 -3pqr = 4. If a =q+r, b=r+p and 
c=p+q, then what is the value of a
3
+b
3
+c
3
 – 
3abc?  
  p
3
+q
3
+r
3
–3pqr = 4 nw~ Ùeefo a =q+r, b=r+p Deewj 
c=p+q nQ, lees a
3
+b
3
+c
3
 – 3abc keâe ceeve keäÙee nw?  
 (a) 4  (b) 8  
 (c) 2 (d) 12 
14.  If a and ß are the roots of the equation x
2
+x-
1=0, then what is the equation whose roots are 
a
5
 and ß
5
?  
  Ùeefo a leLee ß meceerkeâjCe x
2
+x–1=0, kesâ cetue nQ, lees Jen 
meceerkeâjCe keäÙee nw efpemekesâ cetue a
5
 leLee ß
5 
nw? 
 (a) x
2
+7x –1 = 0   (b) x
2
–7x –1 = 0     
 (c) x
2
–11x –1 = 0  (d) x
2
+11x –1 = 0  
15.  If x and y are natural numbers such that x + y 
= 2017, then what is the value of (-1)
x
 + (–1)
y
?  
  Ùeefo x leLee y Øeeke=âeflekeâ mebKÙeeSB Fme Øekeâej nw efkeâ x + 
y = 2017 nw, lees (-1)
x
 + (–1)
y 
keâe ceeve keäÙee nw?  
 (a) 2   (b) –2  
 (c) 0 (d) 1 
16.  If x + (1/x) = ( 3 +1)/2, then what is the value 
of x
4
+(1/x
4
)?  
  Ùeefo x + (1/x) = ( 3 +1)/2 nw, lees x
4
+(1/x
4
)? keâe 
ceeve keäÙee nw?  
 (a) 
( )
4 3 1 / 4 - (b) 
( )
4 3 1 / 2 +  
 (c) 
( )
4 3 1 / 4 - - (d) 
( )
4 3 1 / 2 - -  
17.  If a+a
2
+a
3
-1=0, then what is the value of 
a
3
+(1/a)   
  Ùeefo a+a
2
+a
3
-1=0, nes lees a
3
+(1/a) keâe ceeve keäÙee nw? 
 
 
 (a) 1  (b) 4  
 (c) 2 (d) 3 
18.  If a– (1/a) = b, b – (1/b) = c and c – (1/c) =a, 
then what is the value of (1/ab) + (1/bc) + 
(1/ca)?   
  Ùeefo a– (1/a) = b, b – (1/b) = c leLee c = – (1/c) =a 
nwQ, lees (1/ab) + (1/bc) + (1/ca) keâe ceeve keäÙee nw? 
 (a) –3  (b) –6  
 (c) –1 (d) –9 
19.  If the roots of the equation a(b-c)x
2
+b(c–
a)x+c(a-b)=0 are equal, then which of the 
following is true?     
  Ùeefo meceerkeâjCe a(b-c)x
2
+b(c–a)x+c(a-b)=0 kesâ cetue 
yejeyej nw, lees efvecveefueefKele ceW mes keâewve mee mener nw? 
 (a) b=(a+c)/ac   (b) 2/b=(1/a)+(1/c)  
 (c) 2b = (1/a) + (1/c) (d) abc= ab + bc + ca   
20.  If 
? ?
? ?
2 2
(a + b + ab) +
? ?
? ?
2 2
(a + b - ab) =1, then 
what is the value of (1–a
2
)(1–b
2
)?  
   Ùeefo 
? ?
? ?
2 2
(a + b + ab) +
? ?
? ?
2 2
(a + b - ab) =1, nes 
lees (1–a
2
)(1–b
2
) keâe ceeve keäÙee nw? 
 (a) 1/4 (b) 4/7  
 (c) 5/4 (d) 3/4 
21.  If 3x + 4y –11 = 18 and 8x– 6y + 12 = 6, then 
what is the value of 5x–3y – 9?    
  Ùeefo 3x + 4y –11 = 18 leLee 8x– 6y + 12 = 6 nw, lees 
5x–3y – 9 keâe ceeve keäÙee nw? 
 (a) 18  (b) –9   
 (c) –27 (d) –18   
22.  If a +b+c = 7/12,  3a – 4b + 5c = 3/4 and 7a–11b 
– 13c = –7/12 , then what is the value of a+c?  
  Ùeefo a +b+c = 7/12,  3a – 4b + 5c = 3/4 leLee 7a–
11b – 13c = –7/12  nQ, lees a+c keâe ceeve keäÙee nw? 
 (a) 1/2   (b) 5/12  
 (c) 3/4  (d) 1/4 
23.  The given figure, PQ = PS = SR and 
?QPS=40
0
, then what is the value of ?QPR (in 
degrees)?   
  oer ieF& Deeke=âefle ceW, PQ = PS = SR leLee ?QPS=40
0
, 
nes, lees ?QPR keâe ceeve (ef[«eer ceW) keäÙee nw?   
 
 (a) 45  (b) 60  
 (c) 75 (d) 50 
24.  In triangle PQR, C is the centroid, PQ = 30 cm, 
QR = 36 cm and PR = 50 cm. If D is the 
midpoint of QR, then what is the length (in cm) 
of CD?    
  ef$eYegpe PQR ceW C kesâvõkeâ nw~ PQ = 30 mesceer., QR = 
36 mesceer. leLee PR = 50 mesceer. nw~ Ùeefo D, QR keâe 
ceOÙeefyevog nw, lees CD keâer uecyeeF& (mesceer ceW) keäÙee nw?    
 (a) 
( )
4 86 / 3 (b) 
( )
2 86 / 3  
 (c) 
( )
5 86 /3  (d) 
( )
5 86 / 2  
25.  In the given figure, AQ = 4 2 cm, QC = 6 2 
cm and AB = 20 cm. If PQ is parallel to BC, 
then what is the value ( in cm) of PB?  
  oer ieF& Deeke=âefle ceW AQ = 4 2 mesceer, QC = 6 2 mesceer 
leLee AB = 20 mesceer~ Ùeefo PQ, BC kesâ meceeblej nw, lees 
PB keâe ceeve (mesceer ceW) keäÙee nw?  
 
 
 (a) 8  (b) 12  
 (c) 6 (d) 15 
26.  In the given figure, if AD = 12 cm, AE = 8cm 
and EC = 14 cm, then what is the value (in cm) 
of BD?  
  oer ieF& Deeke=âefle ceW AD = 12 mesceer., AE = 8 mesceer leLee 
EC = 14 mesceer nQ, lees BD keâe ceeve (mesceer ceW) keäÙee nw? 
 
 (a) 50/3  (b) 15  
 (c) 8/3 (d) 44/3 
27.  Two circle are having radii 9 cm and 12 cm. 
The distance between their centres is 15cm. 
What is the length (in cm) of their common 
chord?/oes Je=òeeW keâer ef$epÙeeSB 9 mesceer. leLee 12 mesceer nQ~ 
oesveeW kesâ kesâõeW kesâ ceOÙe keâer otjer 15 mesceer nw~ Gvekeâer 
meeceevÙe peerJee keâer uecyeeF& (mesceer. ceW) keäÙee nw?  
 (a) 6.8  (b) 13.6  
 (c) 7.2 (d) 14.4 
28.  Two circle touch each other at point X. Two 
common tangents of the circle meet at point P 
and none of the tangents passes through X. 
These tangents touch the larger circle at points 
B and C. If the radius of the larger circle is 15 
cm and CP = 20 cm, then what is the radius (in 
cm) of the smaller circle?     
  oes Je=òe efyebog X hej Skeâ otmejs keâes mheMe& keâjles nQ~ Je=òeeW 
keâer oes meceeve mheMe&jsKeeSB efyebog P hej efceueleer nw leLee 
keâesF& Yeer mheMe& jsKee X mes veneR iegpejleer nw~ Ùen 
mheMe&jsKeeSb yeÌ[s Je=òe keâes efyebog B leLee C hej mheMe& keâjleer 
nw~ Ùeefo yeÌ[s Je=òe keâer ef$epÙee 15 mesceer leLee  CP = 20 
mesceer nw, lees Úesšs Je=òe keâer ef$epÙee (mesceer ceW) keäÙee nw? 
 (a) 3.5  (b) 3.75  
 (c) 4.25 (d) 4.45 
29.  Two circles touch each other of point X. A 
common tangent touch them at two distinct 
points Y and Z. If another tangent passing 
through X cut YZ at A and XA = 16 cm, then 
what is the vale (in cm) of YZ?    
  oes Je=òe Skeâ -otmejs keâes efyebog X hej mheMe& keâjles nQ~ Skeâ 
meceeve mheMe&jsKee GvnW oes Deueie efyebogDeeW Y leLee Z hej 
mheMe& keâjleer nw~ Ùeefo X mes iegpejves Jeeueer Skeâ DevÙe 
mheMe&jsKee YZ keâes A hej keâešleer nw leLee XA = 16 mesceer 
nw, YZ keâe ceeve (mesceer. ceW) keäÙee nw?  
 (a) 18  (b) 24  
 (c) 16 (d) 32 
30.  There are 8 equidistant points A, B, C, D, E, F, 
G and H (in same order) on a circle. What is 
the value of ?FDH (in degree)?   
  Skeâ Je=òe hej 8 meceeveeblej efyebog A, B, C, D, E, F, G 
leLee H (Fmeer ›eâce ceW) nQ~ ?FDH keâe ceeve (ef[«eer ceW) 
keäÙee nw? 
 (a) 22.5  (b) 45  
 (c) 30 (d) 42.5 
31.  In the Given the figure, O is the centre of the 
circle and ?QOR = 50
0
, then what is the value 
of ?RPQ (in degrees)?  
  oer ieF& Deeke=âefle ceW O Skeâ Je=òe keâe kesâõ nw leLee ?QOR 
= 50
0 
nw, lees ?RPQ keâe ceeve (ef[«eer ceW) keäÙee nw?   
 
 (a) 15  (b) 25  
 (c) 20 (d) 30 
32.  Three circle C
1
, C
2
 and C
3
 with radii r
1
, r
2
 and 
r
3
 (where r
1
 < r
2
 < r
3
) are placed as shown in 
the given figure. What is the value of r
2
?    
  leerve Je=òe C
1
, C
2
 leLee C
3
 efpevekeâer ef$epÙeeSB r
1
, r
2
 leLee 
r
3
 (peneB r
1
 < r
2
 < r
3
) keâes oer ngF& Deeke=âefle ceW oMee&Ùee 
ieÙee nw~ r
2 
keâe ceeve keäÙee nw? 
 
 (a) ( )
1 3
r r  (b) ( )
1 3
r r / 2 +  
 (c) ( ) ( )
1 2 1 2
2r r / r r + (d) ( )
1 3
r r + 
33.  An equilateral triangle of area 300 cm
2
 is cut 
from its three vertices to form a regular 
hexagon. Area of hexagon is what percent of 
the area of triangle?    
  Skeâ meceyeeng ef$eYegpe efpemekeâe #es$eheâue 300 mesceer
2
 nw, 
keâes Gmekesâ leerveeW Meer<eeX mes Skeâ mece<ešYegpe yeveeves kesâ 
efueS keâeše peelee nw~ <ešYegpe keâe #es$eheâue ef$eYegpe kesâ 
#es$eheâue keâe efkeâlevee ØeefleMele nw?   
 (a) 66.66%  (b) 33.33%  
 (c) 83.33% (d) 56.41% 
34.  In the given figure, PQR is an equilateral 
triangle with side as 12 cm. S and T are the mid 
points of the sides PQ and PR respectively. 
What is the area (in cm
2
) of the shaded region?   
  oer ieF& Deeke=âefle ceW, PQR Skeâ meceyeeng ef$eYegpe nw, 
efpemekeâer Yegpee 12 mesceer nw~ S leLee T, ›eâceMe: Yegpee PQ  
leLee PR kesâ ceOÙe efyevog nw~ ÚeÙeebefkeâle Yeeie keâe #es$eheâue 
(mesceer
2
 ceW) keäÙee nw?   
 
 
 (a) 10 3  (b) 12 3  
 (c) 9 3 (d) 14 3 
35.  ABCD is a rectangle. P is a point on the side 
AB as shown in the given figure. If DP = 13. CP 
= 10 and BP = 6, then what is the value of AP?     
  ABCD Skeâ DeeÙele nw~ P, Yegpee AB hej Skeâ efyevog nw, 
pewmee efkeâ oer ieF& Deeke=âefle ceW oMee&Ùee ieÙee nw~ DP = 13. 
CP = 10 Deewj BP = 6 nes, lees  AP keâe ceeve keäÙee nw?  
 
 (a) 105  (b) 133  
 (c) 12 (d) 10 
36.  In the given figure, PQRSTU is a regular 
hexagon of side 12 cm. what is the area (in cm
2
) 
of triangle SQU?  
  oer ieF& Deeke=âefle ceW PQRSTU Skeâ mece<ešYegpe nw 
efpemekeâer Yegpee 12 mesceer. nw~ ef$eYegpe SQU keâe #es$eheâue 
(mesceer
2
ceW) keäÙee nw?  
 
 (a) 162 3 (b) 216 3 
 (c) 108 3  (d) 54 3 
37.  In the given figure, ABCD is a square, BCXYZ 
is a regular pentagon and ABE is an equilateral 
triangle. What is the value ( in degrees) of 
?EBZ?   
  oer ieF& Deeke=âefle cessb, ABCD keâe Jeie& nw, BCXYZ Skeâ 
mece hebÛeYegpe nw leLee ABE Skeâ meceef$eYegpe nw ?EBZ 
keâe ceeve (ef[«eer ceW) keäÙee nw? 
 
 (a) 102  (b) 98  
 (c) 78 (d) 64 
38.  In the given figure, 3 semicircles are drawn on 
three sides of triangle ABC. AB = 21 cm. BC = 
28 cm and AC = 35 cm. What is the area (in 
cm
2
) of the shaded part?  
  oer ieF& Deeke=âefle ceW, ef$eYegpe ABC keâer leerveeW YegpeeDeeW hej 
3 DeOe&Je=òe yeveeÙes ieÙes nQ~ AB = 21 mesceer, BC = 28 
mesceer leLee AC = 35 mesceer~ ÚeÙeebefkeâle Yeeie keâe #es$eheâue 
(mesceer ceW) keäÙee nQ?   
 
 (a) 588  (b) 324  
 (c) 294 (d) 286 
39.  The sum of radii of the two circle is 91 cm and 
the difference between their area in 2002 cm
2
. 
What is the radius (in cm) of the larger circle?   
  oes Je=òeeW keâer ef$epÙeeDeeW keâe Ùeesie 91 mesceer nw leLee Gvekesâ 
#es$eheâue kesâ ceOÙe keâe Deblej 2002 mesceer
2
 nw~ yeÌ[s Je=òe keâer 
ef$epÙee (mesceer ceW) keäÙee nw?   
 (a) 56  (b) 42  
 (c) 63 (d) 49 
40.  A right triangular prism has equilateral 
triangle as its base. Side of the triangle is 15 
cm. Hight of the prism is 20 3 cm. What is the 
volume (in cm
3
) of the?   
  Skeâ uecyeJele ef$eYegpeekeâej efØep]ce keâe DeeOeej meceyeeng 
ef$eYegpe keâer Yegpee 15 mesceer. nw~ efØep]ce keâer TBÛeeF& 
20 3 mesceer. nw~ efØep]ce keâe DeeÙeleve (mesceer.
3
 ceW) keäÙee nw?   
 (a) 1125  (b) 6750  
 (c) 4500 (d) 3375 
41.  The higher of a cone is 45 cm. It is cut at a 
height of 15 cm from its base by a plane 
parallel to its base. If the volume of the smaller 
cone is 18480 cm
3
, then what is the volume (in 
cm
3
) of the original cone?  
  Skeâ Mebkegâ keâer GBâÛeeF& 45 mesceer. nw~ Fmes DeeOeej mes 15 
mesceer Thej Skeâ leue Éeje Gmekesâ DeeOeej kesâ meceeveeblej 
keâeše peelee nw~ Ùeefo Úesšs Mebkegâ keâe DeeÙeleve 18480 
mesceer
3
 nw, lees cetue Mebkegâ keâe DeeÙeleve (mesceer.
3 
ceW) keäÙee nw?  
 (a) 34650  (b) 61600   
 (c) 36960 (d) 62370 
42.  The radio of the curved surface area and total 
surface area of a right circular cylinder is 2:5. 
If the total surface area is 3080 cm
2
, then what 
is the volume (in cm
3
) of the cylinder?     
  Skeâ uecyeJele Je=òeekeâej yesueve kesâ Je›eâ he=<"erÙe #es$eheâue 
leLee kegâue he=<"erÙe #es$eheâue keâe Devegheele 2 : 5 nQ~ Ùeefo 
kegâue he=<"erÙe #es$eheâue 3080 mesceer
2
 nw, lees yesueve keâe 
DeeÙeleve (mesceer
3
 ceW) keäÙee nw?  
 (a) 4312 6  (b) 3822 6  
 (c) 4522 6 (d) 4642 6 
43.  The radius and height of a solid cylinder are 
increased by 2% each. What will be the 
approximate percentage increase in volume?  
  Skeâ "esme yesueve keâer ef$epÙee leLee GBâÛeeF& ØelÙeskeâ keâes 2³ 
mes yeÌ{eÙee peelee nw~ DeeÙeleve ceW ueieYeie efkeâleves ØeefleMele 
keâer Je=efæ nesieer?  
 
 (a) 6.76  (b) 5.88  
 (c) 6.12 (d) 3.34 
44.  A sphere of radius 21 cm is cut into 8 identical 
parts by cuts (1 cut along each axis). What will 
be the total surface area (in cm
2
) of each part?    
  Skeâ 21 mesceer ef$epÙee Jeeues ieesues keâes 3 keâšeJe (ØelÙeskeâ 
De#e hej 1 keâševe) ueieekeâj 8 mece™he YeeieeW ceW keâeše 
peelee nw~ ØelÙeskeâ Yeeie keâe kegâue he=<"erÙe #es$eheâue (mesceer
2
 
ceW) keäÙee nesiee?  
 (a) 844.5  (b) 1732.5  
 (c) 1039.5 (d) 1115.6 
45.  Two identical hemisphere of maximum possible 
size are cut from a solid cube of side 14 cm. The 
bases of the hemispheres are part of the two 
opposite faces of cube. What is the total volume 
(in cm
3
) of the remaining part of cube?  
  oes mece™he DeefOekeâlece mebYeJe ceehe Jeeues DeOe&ieesueeW keâes 
Skeâ 14 mesceer. Yegpee Jeeues "esme Ieve mes keâeše peelee nw~ 
DeOe&ieesueeW kesâ DeeOeej Ieve kesâ oes efJehejerle heâuekeâ kesâ 
Yeeie nw~ Ieve kesâ Mes<e Yeeie keâe kegâue DeeÙeleve (mesceer
3
 ceW) 
keäÙee nw?   
 (a) 1556.33  (b) 898.5  
 (c) 1767.33 (d) 1306.67 
46.  Identical cubes of largest possible size are cut 
from a solid cuboid of size 65 cm × 26 cm × 3.9 
cm. What is the total surface are (in cm
2
) of all 
the small cubes together?     
  Skeâ "esme IeveeYe efpemekeâe ceehe 65 mesceer × 26 mesceer × 
3.9 mesceer nw, mes DeefOekeâlece mebYeJe ceehe Jeeues mece™he 
IeveeW keâes keâeše ieÙee~ meYeer Úesšs IeveeW keâe efceueekeâj kegâue 
he=<"erÙe #es$eheâue (mesceer
2
 ceW) keäÙee nw?  
 (a) 30420  (b) 32001  
 (c) 20280 (d) 16440 
47.  A regular triangular pyramid is cut by 2 planes 
which are parallel to its base. The planes trisect 
the altitude of the pyramid. Volume of top. 
middle and bottom part is V
1
, V
2
 and V
3
 
respectively. What is the value of V
1
 : V
2
, V
3
?    
  Skeâ mece ef$eYegpeekeâej efhejeefce[ keâes oes leue pees Gmekesâ 
DeeOeej kesâ meceeblej nQ, Éeje keâeše peelee nw~ leue 
efhejeefce[ keâer GBâÛeeF& keâes meceef$eYeeefpele keâjles nQ~ Gmekesâ 
Thejer, ceOÙe leLee efveÛeues Yeeie keâe DeeÙeleve ›eâceMe V
1
, 
V
2
 leLee V
3
 nw~  V
1
 : V
2
, V
3 
keâe ceeve keäÙee nw? 
 (a) 1 : 8 : 27  (b) 1 : 8 : 19 
 (c) 2 : 9 : 27 (d) 1 : 7 : 19 
48.  What is the value of [(cos 7A+cos 5A) ÷ sin 7A–
sin 5A)]?  
  [(cos 7A+cos 5A) ÷ sin 7A–sin 5A)] keâe ceeve keäÙee nw?  
 (a) tan A   (b) tan 4 A  
 (c) cot 4 A  (d) cot A  
49.  What is the value of [1–sin(90-2A)]/ 
[1+sin(90+2A)]?  
  [1–sin(90-2A)]/ [1+sin(90+2A)] keâe ceeve keäÙee nw?  
 (a) sin A cos A  (b) cot
2
A  
 (c) tan
2
A (d) sin
2
A cos A 
50.  What is the value of sin 75
0
 + sin 15
0
?  
  sin 75
0
 + sin 15
0 
keâe ceeve keäÙee nw?  
 (a) 3 (b) 2 3  
 (c) 
( )
3/ 2  (d) 3/ 2  
51.  What is the value of [cos 3? + 2cos5? + cos 7?) 
÷ (cos ?+ 2 cos 3? + cos5?)] + sin 2? tan 3??  
  [cos 3? + 2cos5? + cos 7?) ÷ (cos ?+ 2 cos 3? + 
cos5?)] + sin 2? tan 3? keâe ceeve keäÙee nw? 
 (a) cos 2?  (b) sin 2?  
 (c) tan 2? (d) cot ? sin 2? 
52.  What is the value of [2 sin (45+?) sin (45-?)]/cos 
2??  
  [2 sin (45+?) sin (45-?)]/cos 2? keâe ceeve keäÙee nw? 
 (a) 0  (b) tan 2?  
 (c) cot 2? (d) 1 
53.  What is the value of sin (90
0
+2A) [4 – (cos
2
(90
0
-
2A)]?  
  sin (90
0
+2A) [4 – cos
2
(90
0
-2A)] keâe ceeve keäÙee nw?   
  (a) 4(cos
3
A–sin
3
A)  (b) 4(cos
3
A+sin
3
A)   
 (c) 4(cos
6
A+sin
6
A)  (d) 4(cos
6
A–sin
6
A)  
54.  What is the value of [cos (90+A) ÷ sec (270–A) 
+ [sin 270 + A) ÷ cosec (630–A)]?  
  [cos (90+A) ÷sec (270–a) + [sin 270 + A) ÷cosec 
(630–A)] keâe ceeve keäÙee nw? 
 (a) 3 sec A   (b) tan A sec A   
 (c) 0  (d) 1  
55.  On walking 100 metres towards a building in a 
horizontal line, the angle of elevation of its top 
changes from 45
0
 to 60
0
. What will be the 
height (in metres) of the building?     
  Skeâ Fceejle keâer Deesj #eweflepe jsKee ceW 100 ceeršj Ûeueves 
mes Gmekeâer Ûeesšer keâe GVeÙeve keâesCe 45
0
 mes 60
0 
nes peelee 
nw~ Fceejle keâer TBÛeeF& (ceeršj ceW) keäÙee nesieer?  
 (a) 
( )
50 3 3 +   (b) 
( )
100 3 1 +  
 (c) 150 (d) 100 3 + 
56.  The upper part of a tree broken over by the 
wind make an angle of 60
0
 with the ground. 
The distance between the root and the point 
where top of the tree touches the ground is 25 
meters. What was the height ( in meter) of the 
tree?   
  Skeâ Je=#e keâe Thejer Yeeie DeeBOeer kesâ keâejCe štškeâj Yetefce 
keâer melen mes 60
0 
keâe keâesCe yeveelee nw~ peÌ[ Deewj efpeme 
efyevog hej Je=#e keâe Meer<e& Yetefce keâes Útlee nw kesâ ceOÙe otjer 
25 ceeršj nw~ Je=#e keâer TBÛeeF& (ceeršj ceW) keäÙee Leer?  
 (a) 84.14  (b) 93.3  
 (c) 98.25 (d) 120.24 
57.  The height of a towar is 300 metres. When its 
top is seen from top of another towar, then the 
angle of depression of 60
0
. The horizontal 
distance between the bases of the two towers is 
120 metres. What is the height ( in meters) of 
the small tower?